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The product of two consecutive positive integers is 1,332. Explain how you can write and solve a quadratic equation to find the value of the larger integer.

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Answer:

The numbers can be written as x and x + 1. Set the product of the numbers equal to 1,332 to get x(x + 1) = 1,332. You can solve the quadratic equation by using the quadratic formula, completing the square, or factoring. When you solve the quadratic equation, you find that x = –37 and 36. Since the question asked for positive integers, the only viable solution is x = 36. To solve for the larger integer, you add 1 to 36 to get an answer of 37.

Step-by-step explanation:

sample response

The first consecutive number is 36 and the second consecutive number is 37.

What are the consecutive numbers?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

Let the first consecutive number be x and the second consecutive number be (x+1).

The product of two consecutive positive integers is 1,332.

[tex]\rm x\times (x+1)=1332\\\\x^2+x=1332\\\\x^2+x-1332=0\\\\x^2+37x-36x-1332=0\\\\x(x+37)-36(x+37x)=0\\\\(x+37)(x-36)=0\\\\x+37=0, \ x=-37\\\\x-36=0, \ x=36[/tex]

(Ignoring the negative value of x).

The first consecutive number = x = 36

The second consecutive number = x+1 = 36 + 1 = 37

Hence, the first consecutive number is 36 and the second consecutive number is 37.

Learn more about consecutive numbers here;

https://brainly.com/question/12556742

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